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3.1.6 - The influence of gravity

The potential energy of water is affected by gravity: unconstrained water runs down hill. In most plants the effect of gravity is small relative to common values of the water potential, but in tall trees it can dominate. Where the effect is important it is convenient to introduce the notion of a total water potential, \( Φ \), which is the sum of the water potential, \( ψ \), and a gravitational term, thus

\[\Phi = \psi + \rho gh = P - \pi + \rho gh \tag{7}\]

where \( ρ \) (kg m-3) is the density of water, \( g \) (m s-2) is the acceleration due to gravity, and \( h \) (m) is the height (relative to some reference) in the gravitational field. \( Φ \) is constant in a system at equilibrium with respect to water even when height varies. The value of \( g \) is approximately 10 m s-2, so the gravitational term, \( ρgh \), increases by 10 kPa for each metre increase in height. Hence, at equilibrium, when \( Φ \) and \( π \) are uniform (at least, in a system without semipermeable membranes) the hydrostatic pressure falls by 10 kPa for each metre increase in height.

In the tallest trees, for example a Eucalyptus regnans 100 m tall, equation (6) predicts that, even when the tree is not transpiring, the water potential at the top is about 1.0 MPa lower than at the base.